octonion

non-commutative, non-associative algebra of numbers with eight real components

Wikidata entity: Q743418

Wikimedia Commons category is Octonions

P373	Commons category	String	Octonions	???
P2534	defining formula	Math	$\begin{aligned} 𝕆 & = {a_{0} + a_{1} e_{1} + \dots + a_{7} e_{7} ∣ a_{0}, \dots, a_{7} \in ℝ} \\ e_{i} e_{j} & = - δ_{i j} + c_{i j k} e_{k} \\ c_{i j k} & = {\begin{cases} 1 & even perm. of 123, 145, 176, 246, 257, 347, 365 \\ - 1 & odd perm. of 123, 145, 176, 246, 257, 347, 365 \\ 0 & otherwise \end{cases} \end{aligned}$	???
P61	discoverer or inventor	...	Q940427 (John T. Graves)	John T. Graves
P156	followed by	...	Q79188 (sedenion)	sedenion
P155	follows	...	Q173853 (quaternion)	quaternion
P527	has part(s)	...	Q173853 (quaternion)	quaternion
P7235	in defining formula	Math	$e_{i}$	???
P7235	in defining formula	Math	$δ_{i j}$	???
P31	instance of	...	Q2165111 (alternative algebra)	alternative algebra
P31	instance of	...	Q2835924 (octonion algebra)	octonion algebra
P6104	maintained by WikiProject	...	Q8487137 (WikiProject Mathematics)	WikiProject Mathematics
P361	part of	...	Q2835924 (octonion algebra)	octonion algebra
P5555	schematic	CommonsMedia	http://commons.wikimedia.org/wiki/Special:FilePath/Octonion-Multiplication-Table.png	???
P1482	Stack Exchange tag	Url	Newest 'octonions' Questions - Mathematics Stack Exchange	???
P1482	Stack Exchange tag	Url	Newest 'octonions' Questions - MathOverflow	???
P279	subclass of	...	Q837414 (hypercomplex number)	hypercomplex number
P575	time of discovery or invention	...	1843-01-01	???
P910	topic's main category	...	Q10179671 (Category:Octonions)	Category:Octonions

External Ids

P268	Bibliothèque nationale de France ID	15608111r
P2163	FAST ID	849971
P646	Freebase ID	/m/0dkps
P227	GND ID	4745179-8
P269	IdRef ID	122706331
P244	Library of Congress authority ID	sh2002008702
P2812	MathWorld ID	CayleyNumber
P2812	MathWorld ID	Octonion
P6366	Microsoft Academic ID (discontinued)	2779181008
P8885	Namuwiki ID	팔원수
P8189	National Library of Israel J9U ID	987007558916605171
P4215	nLab ID	octonion
P6781	ProofWiki ID	Definition:Octonion
P10376	ScienceDirect topic ID	mathematics/octonions
P13591	Yale LUX ID	concept/55f53b31-2e07-4558-b872-9767f8de88cc

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